Particle Worldline Model Documents

Main Document

The Particle Worldline model computes and displays the trajectory of a test particle in the vicinity of a black hole using Schwarzschild coordinates. It was created for the study of Einstein's theory of general relativity and the Schwarzschild metric.

The model has input fields displaying the Schwarzschild coordinates and their rates of change as well as the energy E and and angular momentum L of the particle. Conservation laws and the speed of light impose restrictions on the dynamical variables and these restrictions are enforced when entering values or dragging the particle. For example, if a user changes the default value of dr/dt to 10, the model automatically reduces the value to 0.685 because the particle speed cannot exceed the speed of light c=1.

The Particle Worldline model a supplemental simulation for the article "When action is not least for orbits in general relativity" by C. G. Gray and Eric Poisson in the American Journal of Physics 79(1), 43-55 (2011) and has been approved by the authors and the American Journal of Physics (AJP) editor. The simulation was developed using the Easy Java Simulations (EJS) modeling tool and is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_gr_ParticleWorldline.jar file will run the program if Java is installed.